Professor Roy's research includes cellular automata, complex systems, and theoretical computer science, with a focus on the effect of perturbation in cellular automata. Currently, he is exploring the broad research question - "Does robust computation exist?" where he tries to solve real computational problems and technological solutions with the effect of noise. With this, he tries to understand the big philosophical question - "Does nature compute?". In particular, he is interested in models which make use of randomness to perform robust computation.
In this doctoral dissertation, he investigated distributed computing on cellular automata with application to societal problems which includes theoretical solutions of distributed computing problems and modeling societal distributed phenomena like riots using cellular automata. In his master's dissertation, he explored the theoretical properties of convergent discrete dynamical systems with the effect of noise.
He has also explored art, patterns, and computation, with a focus on patterns of chaotic systems, and symmetries within them. Professor Roy's computational patterns are exhibited in the Indian School of Logic and its applications, Asian Symposium on Cellular Automata Technology.
Professor Roy's research interest also includes the history and philosophy of computation. In this context, he is one of the co-authors of the book "The Mathematical Artist - A Tribute to John Horton Conway".